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Regression of Area Mortality Rates on Expalanatory Variables: What Weighting is Appropriate?

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  • Stuart J. Pocock
  • Derek G. Cook
  • Shirley A. A. Beresford

Abstract

One can often gain insight into the aetiology of a disease by relating mortality rates in different areas to explanatory variables. Multiple regression techniques are usually employed, but unweighted least squares may be inappropriate if the areas vary in population size. Also, a fully weighted regression, with weights inversely proportional to binomial sampling variances, is usually too extreme. This paper proposes an intermediate solution via maximum likelihood which takes account of three sources of variation in death rates: sampling error, explanatory variables and unexplained differences between areas. The method is also adapted for logit (death rates), standardized mortality ratios (SMRs) and log (SMRs). Two examples are presented.

Suggested Citation

  • Stuart J. Pocock & Derek G. Cook & Shirley A. A. Beresford, 1981. "Regression of Area Mortality Rates on Expalanatory Variables: What Weighting is Appropriate?," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(3), pages 286-295, November.
    • Handle: RePEc:bla:jorssc:v:30:y:1981:i:3:p:286-295
    DOI: 10.2307/2346353
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    Citations

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    Cited by:

    1. Peter Congdon, 1990. "Issues in the Analysis of Small Area Mortality," Urban Studies, Urban Studies Journal Limited, vol. 27(4), pages 519-536, August.
    2. Aregay, Mehreteab & Shkedy, Ziv & Molenberghs, Geert, 2013. "A hierarchical Bayesian approach for the analysis of longitudinal count data with overdispersion: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 233-245.
    3. M L Senior & S J New & A C Gatrell & B J Francis, 1993. "Geographic Influences on the Uptake of Infant Immunisations: 1. Concepts, Models, and Aggregate Analyses," Environment and Planning A, , vol. 25(3), pages 425-436, March.
    4. Michael Tiefelsdorf & Daniel A Griffith, 2007. "Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach," Environment and Planning A, , vol. 39(5), pages 1193-1221, May.
    5. Carlos Díaz-Venegas, 2014. "Identifying the Confounders of Marginalization and Mortality in Mexico, 2003–2007," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 118(2), pages 851-875, September.
    6. Dankmar Böhning & Uwe Malzahn & Jesus Sarol & Sasivimol Rattanasiri & Annibale Biggeri, 2002. "Efficient Non-Iterative and Nonparametric Estimation of Heterogeneity Variance for the Standardized Mortality Ratio," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 827-839, December.
    7. Jordan, Paul, 1995. "Estimation of tolerance limits from reference data," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 655-668, June.
    8. Martin Gächter & Engelbert Theurl, 2010. "Convergence of the Health Status at the Local Level: Empirical Evidence from Austria," NRN working papers 2010-09, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
    9. P Congdon, 1993. "Approaches to Modelling Overdispersion in the Analysis of Migration," Environment and Planning A, , vol. 25(10), pages 1481-1510, October.

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